The ability to detect and respond to spatial gradients of signaling molecules is fundamental for many biological processes in eukaryotic cells, such as differentiation, migration and morphogenesis. While much is known about the proteins that are required for signal transduction and gradient sensing, the precise mechanism by which they interact to transmit information about the environment and create internal gradients of protein activity remain unclear. This proposal seeks to establish the role of receptor endocytosis in modulating signaling activity and gradient sensing in the mating response of Saccharomyces cerevisiae (yeast). Yeast undergo a developmental decision based on the concentration of pheromone. At high pheromone levels, they growth arrest and generate a mating projection (shmoo morphology). At intermediate concentrations they elongate in the direction of an increasing pheromone gradient (chemotrophic growth). This decision requires that the mating response pathway transmit quantitative information about the external pheromone concentration. Through a combination of mathematical modeling and experimental analysis we accumulated strong evidence to support the idea that information about pheromone concentration is transmitted not as the amplitude of signal activity but as signal duration. One goal of this proposal is to test the hypothesis that receptor endocytosis plays an important role in this dose-to-duration conversion. Several experimental and theoretical investigations have suggested that receptor endocytosis is important for establishing cell polarity. Recent theoretical investigations also have suggested that receptor endocytosis increase cell's ability to detect external gradients of signaling molecules. A second goal is to test the hypothesis that receptor endocytosis increases yeast's ability to detect pheromone gradients and track gradients that change in time. The specific aims are: Aim 1. Characterize the role of receptor endocytosis in modulating signal activity. This aim tests the hypothesis that receptor endocytosis provides a mechanism for dose-to-duration encoding. Mathematical modeling is combined with experimental approaches to compare signal activity and responses in wild-type and defined mutant strains of yeast. Aim 2. Characterize the role of receptor endocytosis in gradient sensing. This aim uses mathematical and experimental approaches to test the hypothesis that receptor endocytosis increases yeast's ability to detect a pheromone gradient. Aim 3. Characterize yeast's ability to respond to changing external conditions. This aim tests the hypothesis that receptor endocytosis allows yeast to track time-dependent pheromone gradients. Our recent development of a microfluidics device that allows the direction of a gradient to be modulated in time is a critical feature of our experimental design for investigating yeast's ability to track changing environmental conditions.